Abstract:
Quantum cohomology is considered as a semi-infinite cohomology on the universal cover of free loop spaces. Givental conjectured that the S1-equivariant version of this semi-infinite cohomology should have a D-module structure and recover the ring structure of qunatum cohomolgy in some limit. Here, S1 acts on free loop spaces by rotaion of loops. In this talk, using an algebraic model for free loop spaces of toric varieties, I discuss the construction of semi-infinite equivariant cohomology and its relation to quantum cohomology. If I have time, I would like to touch also on the K-theoreric version.
